We present exact calculations of the zero-temperature partition function, $Z(G,q,T=0)$, and ground-state degeneracy (per site), $W({ G},q)$, for the $q$-state Potts antiferromagnet on a number of families of graphs ${ G}$ for which the boundary ${ \cal B}$ of regions of analyticity of $W$ in the complex $q$ plane is noncompact and has the properties that (i) in the $z=1/q$ plane, the point $z=0$ is a multiple point on ${ \cal B}$ and (ii) ${ \cal B}$ includes support for $Re(q) < 0$. These families are generated by the method of homeomorphic expansion. Our results give further insight into the conditions for the validity of large--$q$ series expansions for the reduced function $W_{ red.}=q^{ -1}W$.
Categories: cond-mat.stat-mech hep-lat math.CO